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Turbulent and Viscous Air Friction in the Mid-High Frequency Loudspeaker

Mid-high frequency loudspeaker with resonant frequency f = 982 Hz has been studied in atmospheres of air, He4, D2 and H2 at pressures ranging 0-1 bar. The measurements of viscous and turbulent contributions to the friction entering Q-factor showed significant difference as compared to a low frequency loudspeaker. The resonant frequency in air is considerably lower in an evacuated space than at 1 bar, and this differs from the low frequency loudspeaker, when opposite is true. Measurements showed that imaginary part of viscous friction in Navier-Stokes equation is dominant, while contribution of the real part to the friction term is less significant, and Navier-Stokes equation reduces to the Stokes form grad p =- mi delta v, when imaginary part of the viscous force reduces effective vibration mass, which in turn enables operation of the loudspeaker at high frequency. The data were interpreted in terms of Greenspan theory of the piston radiator.